Question

(a^(-5)b^(7)c^(3))^(2)-:(a^(4)b^(-2)c^(2))^(3) What are the powers of a b and c

Answer 1

Answer:

The powers of a,b and c for the given expression

$\frac{(a^{-5}b^7c^3)^2}{(a^4b^{-2}c^2)^3}=a^{-22}b^{20}c^0}$ is -22,20 and 0 respectively

Step-by-step explanation:

Given expression is  $\frac{(a^{-5}b^7c^3)^2}{(a^4b^{-2}c^2)^3}$

To find the powers of a,b and c:

$\frac{(a^{-5}b^7c^3)^2}{(a^4b^{-2}c^2)^3}=\frac{(a^{-5})^2(b^7)^2(c^3)^2}{(a^4)^3(b^{-2})^3(c^2)^3}$ ( using the property $(ab)^m=a^m.b^m$ )

$=\frac{a^{-10}b^{14}c^6}{a^{12}b^{-6}c^6}$ ( using the property $(a^m)^n=a^{mn}$ )

$=a^{-10}b^{14}c^6.a^{-12}b^{6}c^{-6}$ ( using the property $\frac{1}{a^m}=a^{-m}$ )

$=a^{-10-12}b^{14+6}c^{6-6}$ ( using the property $a^m.a^n=a^{m+n}$ )

$=a^{-22}b^{20}c^{0}$

Therefore$\frac{(a^{-5}b^7c^3)^2}{(a^4b^{-2}c^2)^3}=a^{-22}b^{20}c^{0}$

The powers of a,b and c for the given expression

$\frac{(a^{-5}b^7c^3)^2}{(a^4b^{-2}c^2)^3}=a^{-22}b^{20}c^0}$ is -22,20 and 0 respectively